A 40 mA current is carried by a uniformly bound air-core solenoid with 450 turns, a 15 mm diameter, and 12 cm length. compute

(a) magnetic field inside the solenoid.

(b) magnetic flux through each turns.

(c) Inductance of solenoid

(d) If the current were different, which of these quantities will change?

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SumantLv10

14 Nov 2020

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A solenoid consists of N = 110 turns of wire length d= 6 cm and cross-sectional area A = 3 cm². Assume that the magnetic field inside the solenoid and ignore end effects.

(a) Write an equation for the magnetic field B produced by the solenoid. Express the answer in terms of the current through the coil I, the number of turns N, length of the coil d, and permeability of free space .

(b) Using the equation for the magnetic field determined in part (a), calculated the magnetic flux, in webers, through a single loop of the solenoid with a current of I = 1.9 A. The coil is d = 6 cm long and has a cross-sectional area of 3 cm² and consists of 110 turns.

(c) The self inductance related the magnetic flux linkage to the current through the coil. Calculate the self inductance L in units of . THe coil is d = 6 cm long and has a cross-sectional area A = 3 cm² and consists of N =110 turns.

orchidmole54

Magnetic Field inside a Very Long Solenoid Learning Goal: To apply Ampère's law to find the magnetic field inside an infinite solenoid. In this problem we will apply Ampère's law. To calculate the magnetic field inside a very long solenoid (only a relatively short segment of the solenoid is shown in the pictures). The segment of the solenoid shown in (Figure 1) has length L, diameter D, and n turns per unit length with each carrying current I. It is usual to assume that the component of the current along the z-axis is negligible. (This may be assured by winding two layers of closely spaced wires that spiral in opposite directions.) From symmetry considerations, it is possible to show that far from the ends of the solenoid, the magnetic field is axial.

A) What is Iencl, the current passing through the chosen loop?

B) Find Bin, the z component of the magnetic field inside the solenoid where Ampère's law applies.

apricotgrasshopper940

Problem Details

Magnetic Field inside a Very Long Solenoid Learning Goal: To apply Ampère's law to find the magnetic field inside an infinite solenoid. In this problem we will apply Ampère's law to calculate the magnetic field inside a very long solenoid (only a relatively short segment of the solenoid is shown in the pictures). The segment of the solenoid shown in (Figure 1) has length L, diameter D, and n turns per unit length with each carrying current I. It is usual to assume that the component of the current along the z axis is negligible. (This may be assured by winding two layers of closely spaced wires that spiral in opposite directions.) From symmetry considerations, it is possible to show that far from the ends of the solenoid, the magnetic field is axial.

Part D

What is Iencl, the current passing through the chosen loop?

Express your answer in terms of L (the length of the Ampèrean loop along the axis of the solenoid) and other variables given in the introduction.

Part E

Find Bin, the z component of the magnetic field inside the solenoid where Ampère's law applies.

Express your answer in terms of L, D, n, I, and physical constants such as ?